commit cd0e8a29ede3335c410f0893b32b54684ea88643
parent 56d4ae91712dcb8b3a151db2e8af3f97af6c5e10
Author: Mikolai Gütschow <mikolai.guetschow@tu-dresden.de>
Date: Wed, 8 Apr 2026 11:56:43 +0200
protocol: factor out and document common functions
Diffstat:
2 files changed, 449 insertions(+), 386 deletions(-)
diff --git a/draft-guetschow-taler-protocol.md b/draft-guetschow-taler-protocol.md
@@ -60,10 +60,15 @@ Use at your own risk!
- `len(a)` denotes the length in bytes of the byte string a
- `padZero(y, a)` denotes the byte string a, zero-padded to the length of y bytes
- `bits(x)`/`bytes(x)` denotes the minimal number of bits/bytes necessary to represent the multiple precision integer x
-- `uint(y, x)` denotes the `y` least significant bits of the integer `x` encoded in network byte order (big endian)
-- `uint16(x)`/`uint32(x)`/`uint64(x)`/`uint256(x)`/`uint512(x)` is equivalent to `uint(16, x)`/`uint(32, x)`/`uint(64, x)`/`uint(256, x)`/`uint(512, x)`, respectively
+- `uint(y, x)` denotes the `y` least significant bits of the integer `x`, zero-padded and encoded in network byte order (big endian)
+- `uintY(x)` where `Y` is a positive integer number is equivalent to `uint(Y, x)`
- `random(y)` denotes a randomly generated sequence of y bits
- `a * b (mod N)` / `a ** b (mod N)` denotes the multiplication / exponentiation of multiple precision integers a and b, modulo N
+- `for`, `if`, variable assignment `=`, and conditional operators are to be interpreted like their Python/Julia equivalents
+- `data.key` denotes the property `key` on the object `data`
+- `0..n` denotes the exclusive range of integer numbers from `0` to `n-1`
+- `⟨dataᵢ⟩` within a context of `i = 0..n` denotes `n` objects `dataᵢ`, represented in memory as a continuous array
+- `⟨dataᵢ.key⟩` within a context of `i = 0..n` denotes an array of the `n` properties `key` of all `n` objects `dataᵢ`
# Cryptographic Primitives
@@ -342,7 +347,7 @@ out = (data == exp)
# Datatypes and Notation
-## Amount
+## Amounts {#amounts}
Amounts are represented in Taler as positive fixed-point values
consisting of `value` as the non-negative integer part of the base currency,
@@ -389,21 +394,32 @@ out = uint32(len(msg)) | uint32(purpose) | msg
## Helper Functions
+There are a certain number of functions which are often needed,
+and therefore omit the typical function syntax of using parentheses:
+
+- `Knows data` specifies `data` that is known a priori at the start of the protocol operation
+- `Check cond` verifies that the boolean condition or variable `cond` is true,
+ or aborts the protocol operation otherwise
+- `Persist data` persists the given `data` to the local database
+- `data = Lookup by key` retrieves previously persisted `data` by the given `key`
+- `Sum ⟨dataᵢ⟩` is valid for numerical objects `dataᵢ` including amounts (cf. {{amounts}}),
+ and denotes the numerical sum of these objects
+
+Some more functions that are used throughout {#protocol}:
+
~~~
-- Denom-Hash: SHA-512(uint32(0) | uint32(1) | denomᵢ.pub)
-- Planchet-Hash: SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
-- check-decrement: check reserve.balance >= total, persist reserve.balance -= total
-- refresh-derivation (only for refresh/link)
-- persist-{type} (key1, key2, ...) => (val1, val2, ...)
-- lookup-{type} (key1)
-- check bool
-- knows data
-- sum ⟨dataᵢ⟩
-- ⟨dataᵢ⟩
-- for/if
+Hash-Denom(denom) =
+ SHA-512(uint32(0) | uint32(1) | denom.pub)
+
+Hash-Planchet(planchet, denom) =
+ SHA-512( SHA-512( denom.pub ) | uint32(0x1) | planchet )
+
+Check-Subtract(value, subtrahend) =
+ Check value >= subtrahend
+ Persist value -= subtrahend
~~~
-# The Taler Crypto Protocol
+# The Taler Crypto Protocol {#procotol}
## Withdrawal {#withdrawal}
@@ -418,7 +434,7 @@ must be smaller or equal to the amount stored in the single reserve used for wit
~~~
wallet exchange
-knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
+Knows ⟨denomᵢ⟩ Knows ⟨denomᵢ.priv⟩
| |
+-----------------------------+ |
| (W1) reserve key generation | |
@@ -428,7 +444,7 @@ knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
| (subject: reserve.pub, amount: value) |
| |
| +------------------------------+
- | | persist (reserve.pub, value) |
+ | | Persist (reserve.pub, value) |
| +------------------------------+
| |
+-----------------------------------+ |
@@ -456,7 +472,7 @@ where (for RSA, without age-restriction)
(W1) reserve key generation (wallet)
reserve = EdDSA-Keygen()
-persist (reserve, value)
+Persist (reserve, value)
~~~
The wallet derives coins and blinding secrets using a HKDF from a single seed per withdrawal operation,
@@ -470,18 +486,18 @@ and might be chosen to be implemented differently.
(W2) coin generation and blinding (wallet)
batch_seed = random(256)
-persist batch_seed
+Persist batch_seed
for i in 0..n:
coin_seedᵢ = HKDF(uint32(i), batch_seed, "taler-withdrawal-coin-derivation", 64)
blind_secretᵢ = coin_seedᵢ[32:]
coinᵢ.priv = coin_seedᵢ[:32]
coinᵢ.pub = EdDSA-GetPub(coinᵢ.priv)
- h_denomᵢ = SHA-512(uint32(0) | uint32(1) | denomᵢ.pub)
+ h_denomᵢ = Hash-Denom(denomᵢ)
planchetᵢ = RSA-FDH-Blind(SHA-512(coinᵢ.pub), blind_secretᵢ, denomᵢ.pub)
- h_planchetᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
+ h_planchetᵢ = Hash-Planchet(planchetᵢ, denomᵢ)
planchets = (⟨h_denomᵢ⟩, ⟨planchetᵢ⟩)
msg = Gen-Msg(WALLET_RESERVE_WITHDRAW,
- ( sum( ⟨denomᵢ.value⟩ ) | sum( ⟨denomᵢ.fee_withdraw⟩ )
+ ( Sum ⟨denomᵢ.value⟩ | Sum ⟨denomᵢ.fee_withdraw⟩
| SHA-512( ⟨h_planchetᵢ⟩ ) | uint256(0x0) | uint32(0x0) | uint32(0x0) ))
sig = EdDSA-Sign(reserve.priv, msg)
~~~
@@ -491,20 +507,19 @@ sig = EdDSA-Sign(reserve.priv, msg)
(⟨h_denomᵢ⟩, ⟨planchetᵢ⟩) = planchets
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
- check denomᵢ known and not withdrawal-expired
- h_planchetᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
+ denomᵢ = Lookup by h_denomᵢ
+ Check denomᵢ known and not withdrawal-expired
+ h_planchetᵢ = Hash-Planchet(planchetᵢ, denomᵢ)
msg = Gen-Msg(WALLET_RESERVE_WITHDRAW,
- ( sum( ⟨denomᵢ.value⟩ ) | sum( ⟨denomᵢ.fee_withdraw⟩ )
+ ( Sum ⟨denomᵢ.value⟩ | Sum ⟨denomᵢ.fee_withdraw⟩
| SHA-512( ⟨h_planchetᵢ⟩ ) | uint256(0x0) | uint32(0x0) | uint32(0x0) ))
-check EdDSA-Verify(reserve.pub, msg, sig)
-check reserve KYC status ok or not needed
-total = sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
-check reserve.balance >= total
-persist reserve.balance -= total
+Check EdDSA-Verify(reserve.pub, msg, sig)
+Check reserve KYC status ok or not needed
+total = Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
+Check-Subtract(reserve.balance, total)
for i in 0..n:
blind_sigᵢ = RSA-FDH-Sign(planchetᵢ, denomᵢ.priv)
-persist withdrawal // todo: what exactly? should be checked first for replay?
+Persist withdrawal // todo: what exactly? should be checked first for replay?
~~~
~~~
@@ -512,10 +527,10 @@ persist withdrawal // todo: what exactly? should be checked first for replay?
for i in 0..n:
coinᵢ.sig = RSA-FDH-Unblind(blind_sigᵢ, blind_secretᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
coinᵢ.h_denom = h_denomᵢ
coinᵢ.blind_secret = blind_secretᵢ // todo: why save blind_secret, if batch_seed already persisted?
-persist ⟨coinᵢ⟩
+Persist ⟨coinᵢ⟩
~~~
## Payment {#payment}
@@ -528,8 +543,8 @@ The payment is complete as soon as the merchant successfully redeems the deposit
~~~
wallet merchant
-knows ⟨coinᵢ⟩ knows merchant.priv
- knows exchange, payto
+Knows ⟨coinᵢ⟩ Knows merchant.priv
+ Knows exchange, payto
| |
| +-----------------------+
| | (M1) order generation |
@@ -577,14 +592,14 @@ where (without age restriction, policy and wallet data hash)
wire_salt = random(128)
determine id, price, info, token?
-persist order = (id, price, info, token?, wire_salt)
+Persist order = (id, price, info, token?, wire_salt)
~~~
~~~
(W1) nonce generation (wallet)
nonce = EdDSA-Keygen()
-persist nonce.priv
+Persist nonce.priv
~~~
Note that the private key of `nonce` is currently not used anywhere in the protocol.
@@ -595,12 +610,12 @@ or proving the payment without resorting to the individual coins.
~~~
(M2) contract generation (merchant)
-check order.token? == token?
+Check order.token? == token?
h_wire = HKDF(wire_salt, payto, "merchant-wire-signature", 64)
determine timestamp, refund_deadline, wire_deadline
contract = (order.{id,price,info,token?}, exchange, h_wire, timestamp, refund_deadline, wire_deadline)
contract.nonce = nonce.pub
-persist contract
+Persist contract
h_contract = SHA-512(canonicalJSON(contract))
msg = Gen-Msg(MERCHANT_CONTRACT, h_contract)
sig = EdDSA-Sign(merchant.priv, msg)
@@ -611,8 +626,8 @@ sig = EdDSA-Sign(merchant.priv, msg)
h_contract = SHA-512(canonicalJSON(contract))
msg = Gen-Msg(MERCHANT_CONTRACT, h_contract)
-check EdDSA-Verify(merchant.pub, msg, sig)
-check contract.nonce == nonce
+Check EdDSA-Verify(merchant.pub, msg, sig)
+Check contract.nonce == nonce
// TODO: double-check extra hash check?
// todo: maybe get rid of CoinSelection altogether by claiming we already know coinᵢ and contributionᵢ
⟨selectionᵢ⟩ = CoinSelection(contract.{exchange,price}) TODO: include MarkDirty here
@@ -626,7 +641,7 @@ for i in 0..n:
| denomᵢ.fee_deposit | merchant.pub | uint512(0x0) ))
sigᵢ = EdDSA-Sign(coinᵢ.priv, msgᵢ)
depositᵢ = (coinᵢ.{pub,sig,h_denom}, contributionᵢ, sigᵢ)
-persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
+Persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
~~~
// TODO: explain CoinSelection
@@ -636,8 +651,8 @@ persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
~~~
(M3) deposit check (merchant)
-check sum( ⟨depositᵢ.contribution⟩ ) == contract.price
-check Deposit(⟨depositᵢ⟩)
+Check Sum ⟨depositᵢ.contribution⟩ == contract.price
+Check Deposit(⟨depositᵢ⟩)
msg = Gen-Msg(MERCHANT_PAYMENT_OK, h_contract)
sig = EdDSA-Sign(merchant.priv, msg)
~~~
@@ -646,7 +661,7 @@ sig = EdDSA-Sign(merchant.priv, msg)
(W3) payment verification (wallet)
msg = Gen-Msg(MERCHANT_PAYMENT_OK, h_contract)
-check EdDSA-Verify(merchant.pub, msg, sig)
+Check EdDSA-Verify(merchant.pub, msg, sig)
~~~
## Deposit {#deposit}
@@ -657,10 +672,10 @@ Deposit could also be used directly by a wallet with its own payto and a minimal
~~~
merchant exchange
-knows exchange.pub knows exchange.priv
-knows merchant.priv knows ⟨denomᵢ⟩
-knows payto, wire_salt |
-knows contract, ⟨depositᵢ⟩ |
+Knows exchange.pub Knows exchange.priv
+Knows merchant.priv Knows ⟨denomᵢ⟩
+Knows payto, wire_salt |
+Knows contract, ⟨depositᵢ⟩ |
| |
+--------------------------+ |
| (M1) deposit preparation | |
@@ -700,8 +715,8 @@ sig = EdDSA-Sign(merchant.priv, msg)
h_wire = HKDF(info.wire.wire_salt, info.wire.payto, "merchant-wire-signature", 64)
for i in 0..n:
coinᵢ = depositᵢ.coin
- denomᵢ = Denom-Lookup(coinᵢ.h_denom)
- check denomᵢ known and not deposit-expired // todo: check could be included in Denom-Lookup
+ denomᵢ = Lookup by coinᵢ.h_denom
+ Check denomᵢ known and not deposit-expired
totalᵢ = depositᵢ.contribution + denomᵢ.fee_deposit
msgᵢ = Gen-Msg(WALLET_COIN_DEPOSIT,
( h_contract | uint256(0x0)
@@ -709,18 +724,17 @@ for i in 0..n:
| info.time.timestamp | info.time.refund_deadline
| totalᵢ
| denomᵢ.fee_deposit | merchant.pub | uint512(0x0) ))
- check EdDSA-Verify(coinᵢ.pub, msgᵢ, depositᵢ.sig)
- check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
- check coinᵢ.value >= totalᵢ
- persist coinᵢ.value -= totalᵢ
-persist deposit-record
+ Check EdDSA-Verify(coinᵢ.pub, msgᵢ, depositᵢ.sig)
+ Check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
+ Check-Subtract(coinᵢ.value, total)
+Persist deposit-record
schedule bank transfer to payto
timestamp = now()
msg = Gen-Msg(EXCHANGE_CONFIRM_DEPOSIT,
( h_contract | h_wire | uint512(0x0)
| timestamp | info.time.wire_deadline
| info.time.refund_deadline
- | sum( ⟨depositᵢ.contribution⟩ )
+ | Sum ⟨depositᵢ.contribution⟩
| SHA-512( ⟨depositᵢ.sig⟩ ) | merchant.pub ))
sig = EdDSA-Sign(exchange.priv, msg)
~~~
@@ -733,19 +747,21 @@ msg = Gen-Msg(EXCHANGE_CONFIRM_DEPOSIT,
( h_contract | h_wire | uint512(0x0)
| timestamp | contract.wire_deadline
| contract.refund_deadline
- | sum( ⟨depositᵢ.contribution⟩ )
+ | Sum ⟨depositᵢ.contribution⟩
| SHA-512( ⟨depositᵢ.sig⟩ ) | merchant.pub ))
-check EdDSA-Verify(exchange.pub, msg, sig)
+Check EdDSA-Verify(exchange.pub, msg, sig)
~~~
## Refresh {#refresh}
// todo: add introductory text
+// todo: factor out Derive (from shared secret onwards)
+
~~~
wallet exchange
-knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
-knows coin |
+Knows ⟨denomᵢ⟩ Knows ⟨denomᵢ.priv⟩
+Knows coin |
| |
+-------------------+ |
| (W1) coin melting | |
@@ -811,19 +827,19 @@ for k in 0..κ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
for i in 0..n:
- h_denomᵢ = SHA-512(uint32(0) | uint32(0x1) | denomᵢ.pub)
+ h_denomᵢ = Hash-Denom(denomᵢ)
planchets = (⟨h_denomᵢ⟩, ⟨planchetₖᵢ⟩, ⟨transferₖᵢ.pub⟩))
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
sig = EdDSA-Sign(coin.priv, msg)
-persist (coin.denom.pub, ...) // todo: double-check
+Persist (coin.denom.pub, ...) // todo: double-check
~~~
{::comment}
@@ -836,35 +852,35 @@ see TEH_handler_melt
~~~
(E1) gamma selection and coin signing (exchange)
-denom = Denom-Lookup(coin.h_denom)
-check denom known and not refresh-expired
-check RSA-FDH-Verify(SHA-512(coin.pub), coin.sig, denom.pub)
-check coin.pub known and dirty
+denom = Lookup by coin.h_denom
+Check denom known and not refresh-expired
+Check RSA-FDH-Verify(SHA-512(coin.pub), coin.sig, denom.pub)
+Check coin.pub known and dirty
(⟨h_denomᵢ⟩, ⟨planchetₖᵢ⟩, ⟨transferₖᵢ.pub⟩)) = planchets
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
- check denomᵢ known and not withdraw-expired
-value' = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
-check value' == value
-check coin.value >= value
-persist coin.value -= value
+ denomᵢ = Lookup by h_denomᵢ
+ Check denomᵢ known and not withdraw-expired
+value' = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
+Check value' == value
+Check-Subtract(coin.value, value)
for k in 0..κ:
for i in 0..n:
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
-check EdDSA-Verify(coin.pub, msg, sig)
-(ɣ, _, _, done, _) = lookup refresh-record(commitment)
-if refresh-record not found:
+Check EdDSA-Verify(coin.pub, msg, sig)
+refresh_record = Lookup by commitment
+(ɣ, _, _, done, _) = refresh_record
+if refresh_record not found:
ɣ = 0..κ at random
for i in 0..n:
blind_sigᵢ = RSA-FDH-Sign(planchetᵧᵢ, denomᵧᵢ.priv)
link_info = (refresh_seed, ⟨transferₖᵢ.pub⟩, ⟨h_denomᵢ⟩, coin_sig)
- persist refresh-record = (commitment, ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, false, link_info)
+ Persist refresh_record = (commitment, ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, false, link_info)
msg = Gen-Msg(EXCHANGE_CONFIRM_MELT,
( commitment | uint32(ɣ) ))
sig = EdDSA-Sign(exchange.priv, msg)
@@ -881,11 +897,11 @@ sig = EdDSA-Sign(exchange.priv, msg)
~~~
(W2) secret revelation (wallet)
-check exchange.pub known
+Check exchange.pub known
msg = Gen-Msg(EXCHANGE_CONFIRM_MELT,
( commitment | ɣ ))
-check EdDSA-Verify(exchange.pub, msg, sig)
-persist refresh-challenge // what exactly?
+Check EdDSA-Verify(exchange.pub, msg, sig)
+Persist refresh-challenge // what exactly?
for k in 0..κ and k != ɣ:
revealed_seedₖ = batch_seedₖ
~~~
@@ -900,8 +916,9 @@ for k in 0..κ and k != ɣ:
~~~
(E2) commitment validation (exchange)
-(ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, done, _) = lookup refresh-record(commitment)
-check not done // todo: sure?
+refresh_record = Lookup by commitment
+(ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, done, _) = refresh_record
+Check not done // todo: sure?
for k in 0..κ and k != ɣ:
⟨transferₖᵢ.priv⟩ = HKDF("refresh-transfer-private-keys", batch_seedₖ, "", n*32)
for i in 0..n:
@@ -912,13 +929,13 @@ for k in 0..κ and k != ɣ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment' = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
-check commitment == commitment'
-persist refresh-record = (_, _, _, true, _)
+Check commitment == commitment'
+Persist refresh_record = (_, _, _, true, _)
~~~
{::comment}
@@ -933,9 +950,9 @@ persist refresh-record = (_, _, _, true, _)
for i in 0..n:
coinᵧᵢ.sig = RSA-FDH-Unblind(blind_sigᵧᵢ, blind_secretᵧᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
coinᵧᵢ.h_denom = h_denomᵢ
- persist ⟨coinᵧᵢ⟩
+ Persist ⟨coinᵧᵢ⟩
~~~
### Link {#link}
@@ -944,7 +961,7 @@ for i in 0..n:
~~~
wallet exchange
-knows coin knows refresh-record for coin
+Knows coin Knows refresh_record for coin
| |
+----------------------+ |
| (W1) history request | |
@@ -988,7 +1005,8 @@ sig = EdDSA-Sign(coin.priv, msg)
~~~
(E1) refresh secret lookup (exchange)
-(ɣ, ⟨blind_sigᵢ⟩, _, done, link_info) = lookup refresh-record(coin.pub)
+refresh_record = Lookup by coin.pub
+(ɣ, ⟨blind_sigᵢ⟩, _, done, link_info) = refresh_record
if done:
melt_info = (ɣ, link_info, ⟨blind_sigᵢ⟩)
else:
@@ -1007,7 +1025,7 @@ else:
(refresh_seed, ⟨transferₖᵢ.pub⟩, ⟨h_denomᵢ⟩, coin_sig) = link_info
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
+ denomᵢ = Lookup by h_denomᵢ
for k in 0..κ:
for i in 0..n:
sharedₖᵢ = ECDH-EdDSA(coin.priv, transferₖᵢ.pub)
@@ -1016,22 +1034,22 @@ for k in 0..κ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
-check EdDSA-Verify(coin.pub, msg, sig)
+Check EdDSA-Verify(coin.pub, msg, sig)
if ⟨blind_sigᵢ⟩ returned:
for i in 0..n:
coinᵧᵢ.sig = RSA-FDH-Unblind(blind_sigᵧᵢ, blind_secretᵧᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
coinᵧᵢ.h_denom = h_denomᵢ
- persist ⟨coinᵧᵢ⟩
+ Persist ⟨coinᵧᵢ⟩
~~~
## Refund {#refund}
diff --git a/draft-guetschow-taler-protocol.xml b/draft-guetschow-taler-protocol.xml
@@ -64,10 +64,10 @@ Use at your own risk!</t>
<t><tt>bits(x)</tt>/<tt>bytes(x)</tt> denotes the minimal number of bits/bytes necessary to represent the multiple precision integer x</t>
</li>
<li>
- <t><tt>uint(y, x)</tt> denotes the <tt>y</tt> least significant bits of the integer <tt>x</tt> encoded in network byte order (big endian)</t>
+ <t><tt>uint(y, x)</tt> denotes the <tt>y</tt> least significant bits of the integer <tt>x</tt>, zero-padded and encoded in network byte order (big endian)</t>
</li>
<li>
- <t><tt>uint16(x)</tt>/<tt>uint32(x)</tt>/<tt>uint64(x)</tt>/<tt>uint256(x)</tt>/<tt>uint512(x)</tt> is equivalent to <tt>uint(16, x)</tt>/<tt>uint(32, x)</tt>/<tt>uint(64, x)</tt>/<tt>uint(256, x)</tt>/<tt>uint(512, x)</tt>, respectively</t>
+ <t><tt>uintY(x)</tt> where <tt>Y</tt> is a positive integer number is equivalent to <tt>uint(Y, x)</tt></t>
</li>
<li>
<t><tt>random(y)</tt> denotes a randomly generated sequence of y bits</t>
@@ -75,6 +75,21 @@ Use at your own risk!</t>
<li>
<t><tt>a * b (mod N)</tt> / <tt>a ** b (mod N)</tt> denotes the multiplication / exponentiation of multiple precision integers a and b, modulo N</t>
</li>
+ <li>
+ <t><tt>for</tt>, <tt>if</tt>, variable assignment <tt>=</tt>, and conditional operators are to be interpreted like their Python/Julia equivalents</t>
+ </li>
+ <li>
+ <t><tt>data.key</tt> denotes the property <tt>key</tt> on the object <tt>data</tt></t>
+ </li>
+ <li>
+ <t><tt>0..n</tt> denotes the exclusive range of integer numbers from <tt>0</tt> to <tt>n-1</tt></t>
+ </li>
+ <li>
+ <t><tt>⟨dataᵢ⟩</tt> within a context of <tt>i = 0..n</tt> denotes <tt>n</tt> objects <tt>dataᵢ</tt>, represented in memory as a continuous array</t>
+ </li>
+ <li>
+ <t><tt>⟨dataᵢ.key⟩</tt> within a context of <tt>i = 0..n</tt> denotes an array of the <tt>n</tt> properties <tt>key</tt> of all <tt>n</tt> objects <tt>dataᵢ</tt></t>
+ </li>
</ul>
</section>
<section anchor="cryptographic-primitives">
@@ -335,8 +350,8 @@ out = (data == exp)
</section>
<section anchor="datatypes-and-notation">
<name>Datatypes and Notation</name>
- <section anchor="amount">
- <name>Amount</name>
+ <section anchor="amounts">
+ <name>Amounts</name>
<t>Amounts are represented in Taler as positive fixed-point values
consisting of <tt>value</tt> as the non-negative integer part of the base currency,
the <tt>fraction</tt> given in units of one hundred millionth (1e-8) of the base currency,
@@ -379,22 +394,42 @@ out = uint32(len(msg)) | uint32(purpose) | msg
</section>
<section anchor="helper-functions">
<name>Helper Functions</name>
+ <t>There are a certain number of functions which are often needed,
+and therefore omit the typical function syntax of using parentheses:</t>
+ <ul spacing="normal">
+ <li>
+ <t><tt>Knows data</tt> specifies <tt>data</tt> that is known a priori at the start of the protocol operation</t>
+ </li>
+ <li>
+ <t><tt>Check cond</tt> verifies that the boolean condition or variable <tt>cond</tt> is true,
+or aborts the protocol operation otherwise</t>
+ </li>
+ <li>
+ <t><tt>Persist data</tt> persists the given <tt>data</tt> to the local database</t>
+ </li>
+ <li>
+ <t><tt>data = Lookup by key</tt> retrieves previously persisted <tt>data</tt> by the given <tt>key</tt></t>
+ </li>
+ <li>
+ <t><tt>Sum ⟨dataᵢ⟩</tt> is valid for numerical objects <tt>dataᵢ</tt> including amounts (cf. <xref target="amounts"/>),
+and denotes the numerical sum of these objects</t>
+ </li>
+ </ul>
+ <t>Some more functions that are used throughout {#protocol}:</t>
<artwork><![CDATA[
-- Denom-Hash: SHA-512(uint32(0) | uint32(1) | denomᵢ.pub)
-- Planchet-Hash: SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
-- check-decrement: check reserve.balance >= total, persist reserve.balance -= total
-- refresh-derivation (only for refresh/link)
-- persist-{type} (key1, key2, ...) => (val1, val2, ...)
-- lookup-{type} (key1)
-- check bool
-- knows data
-- sum ⟨dataᵢ⟩
-- ⟨dataᵢ⟩
-- for/if
+Hash-Denom(denom) =
+ SHA-512(uint32(0) | uint32(1) | denom.pub)
+
+Hash-Planchet(planchet, denom) =
+ SHA-512( SHA-512( denom.pub ) | uint32(0x1) | planchet )
+
+Check-Subtract(value, subtrahend) =
+ Check value >= subtrahend
+ Persist value -= subtrahend
]]></artwork>
</section>
</section>
- <section anchor="the-taler-crypto-protocol">
+ <section anchor="procotol">
<name>The Taler Crypto Protocol</name>
<section anchor="withdrawal">
<name>Withdrawal</name>
@@ -406,7 +441,7 @@ must be smaller or equal to the amount stored in the single reserve used for wit
<t>// todo: extend with extra roundtrip for CBS</t>
<artwork><![CDATA[
wallet exchange
-knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
+Knows ⟨denomᵢ⟩ Knows ⟨denomᵢ.priv⟩
| |
+-----------------------------+ |
| (W1) reserve key generation | |
@@ -416,7 +451,7 @@ knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
| (subject: reserve.pub, amount: value) |
| |
| +------------------------------+
- | | persist (reserve.pub, value) |
+ | | Persist (reserve.pub, value) |
| +------------------------------+
| |
+-----------------------------------+ |
@@ -442,7 +477,7 @@ knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
(W1) reserve key generation (wallet)
reserve = EdDSA-Keygen()
-persist (reserve, value)
+Persist (reserve, value)
]]></artwork>
<t>The wallet derives coins and blinding secrets using a HKDF from a single seed per withdrawal operation,
together with an integer index.
@@ -453,18 +488,18 @@ and might be chosen to be implemented differently.</t>
(W2) coin generation and blinding (wallet)
batch_seed = random(256)
-persist batch_seed
+Persist batch_seed
for i in 0..n:
coin_seedᵢ = HKDF(uint32(i), batch_seed, "taler-withdrawal-coin-derivation", 64)
blind_secretᵢ = coin_seedᵢ[32:]
coinᵢ.priv = coin_seedᵢ[:32]
coinᵢ.pub = EdDSA-GetPub(coinᵢ.priv)
- h_denomᵢ = SHA-512(uint32(0) | uint32(1) | denomᵢ.pub)
+ h_denomᵢ = Hash-Denom(denomᵢ)
planchetᵢ = RSA-FDH-Blind(SHA-512(coinᵢ.pub), blind_secretᵢ, denomᵢ.pub)
- h_planchetᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
+ h_planchetᵢ = Hash-Planchet(planchetᵢ, denomᵢ)
planchets = (⟨h_denomᵢ⟩, ⟨planchetᵢ⟩)
msg = Gen-Msg(WALLET_RESERVE_WITHDRAW,
- ( sum( ⟨denomᵢ.value⟩ ) | sum( ⟨denomᵢ.fee_withdraw⟩ )
+ ( Sum ⟨denomᵢ.value⟩ | Sum ⟨denomᵢ.fee_withdraw⟩
| SHA-512( ⟨h_planchetᵢ⟩ ) | uint256(0x0) | uint32(0x0) | uint32(0x0) ))
sig = EdDSA-Sign(reserve.priv, msg)
]]></artwork>
@@ -473,30 +508,29 @@ sig = EdDSA-Sign(reserve.priv, msg)
(⟨h_denomᵢ⟩, ⟨planchetᵢ⟩) = planchets
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
- check denomᵢ known and not withdrawal-expired
- h_planchetᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetᵢ )
+ denomᵢ = Lookup by h_denomᵢ
+ Check denomᵢ known and not withdrawal-expired
+ h_planchetᵢ = Hash-Planchet(planchetᵢ, denomᵢ)
msg = Gen-Msg(WALLET_RESERVE_WITHDRAW,
- ( sum( ⟨denomᵢ.value⟩ ) | sum( ⟨denomᵢ.fee_withdraw⟩ )
+ ( Sum ⟨denomᵢ.value⟩ | Sum ⟨denomᵢ.fee_withdraw⟩
| SHA-512( ⟨h_planchetᵢ⟩ ) | uint256(0x0) | uint32(0x0) | uint32(0x0) ))
-check EdDSA-Verify(reserve.pub, msg, sig)
-check reserve KYC status ok or not needed
-total = sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
-check reserve.balance >= total
-persist reserve.balance -= total
+Check EdDSA-Verify(reserve.pub, msg, sig)
+Check reserve KYC status ok or not needed
+total = Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
+Check-Subtract(reserve.balance, total)
for i in 0..n:
blind_sigᵢ = RSA-FDH-Sign(planchetᵢ, denomᵢ.priv)
-persist withdrawal // todo: what exactly? should be checked first for replay?
+Persist withdrawal // todo: what exactly? should be checked first for replay?
]]></artwork>
<artwork><![CDATA[
(W3) coin unblinding (wallet)
for i in 0..n:
coinᵢ.sig = RSA-FDH-Unblind(blind_sigᵢ, blind_secretᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
coinᵢ.h_denom = h_denomᵢ
coinᵢ.blind_secret = blind_secretᵢ // todo: why save blind_secret, if batch_seed already persisted?
-persist ⟨coinᵢ⟩
+Persist ⟨coinᵢ⟩
]]></artwork>
</section>
<section anchor="payment">
@@ -508,8 +542,8 @@ where the sum of all contributions (<tt>contributionᵢ <= denomᵢ.value</tt
The payment is complete as soon as the merchant successfully redeems the deposit authorizations at the exchange (cf. <xref target="deposit"/>).</t>
<artwork><![CDATA[
wallet merchant
-knows ⟨coinᵢ⟩ knows merchant.priv
- knows exchange, payto
+Knows ⟨coinᵢ⟩ Knows merchant.priv
+ Knows exchange, payto
| |
| +-----------------------+
| | (M1) order generation |
@@ -555,13 +589,13 @@ knows ⟨coinᵢ⟩ knows merchant.priv
wire_salt = random(128)
determine id, price, info, token?
-persist order = (id, price, info, token?, wire_salt)
+Persist order = (id, price, info, token?, wire_salt)
]]></artwork>
<artwork><![CDATA[
(W1) nonce generation (wallet)
nonce = EdDSA-Keygen()
-persist nonce.priv
+Persist nonce.priv
]]></artwork>
<t>Note that the private key of <tt>nonce</tt> is currently not used anywhere in the protocol.
However, it could be used in the future to prove ownership of an order transaction,
@@ -570,12 +604,12 @@ or proving the payment without resorting to the individual coins.</t>
<artwork><![CDATA[
(M2) contract generation (merchant)
-check order.token? == token?
+Check order.token? == token?
h_wire = HKDF(wire_salt, payto, "merchant-wire-signature", 64)
determine timestamp, refund_deadline, wire_deadline
contract = (order.{id,price,info,token?}, exchange, h_wire, timestamp, refund_deadline, wire_deadline)
contract.nonce = nonce.pub
-persist contract
+Persist contract
h_contract = SHA-512(canonicalJSON(contract))
msg = Gen-Msg(MERCHANT_CONTRACT, h_contract)
sig = EdDSA-Sign(merchant.priv, msg)
@@ -585,8 +619,8 @@ sig = EdDSA-Sign(merchant.priv, msg)
h_contract = SHA-512(canonicalJSON(contract))
msg = Gen-Msg(MERCHANT_CONTRACT, h_contract)
-check EdDSA-Verify(merchant.pub, msg, sig)
-check contract.nonce == nonce
+Check EdDSA-Verify(merchant.pub, msg, sig)
+Check contract.nonce == nonce
// TODO: double-check extra hash check?
// todo: maybe get rid of CoinSelection altogether by claiming we already know coinᵢ and contributionᵢ
⟨selectionᵢ⟩ = CoinSelection(contract.{exchange,price}) TODO: include MarkDirty here
@@ -600,15 +634,15 @@ for i in 0..n:
| denomᵢ.fee_deposit | merchant.pub | uint512(0x0) ))
sigᵢ = EdDSA-Sign(coinᵢ.priv, msgᵢ)
depositᵢ = (coinᵢ.{pub,sig,h_denom}, contributionᵢ, sigᵢ)
-persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
+Persist (contract, ⟨sigᵢ⟩, ⟨depositᵢ⟩)
]]></artwork>
<t>// TODO: explain CoinSelection</t>
<t>// TODO: maybe introduce symbol for pub/priv</t>
<artwork><![CDATA[
(M3) deposit check (merchant)
-check sum( ⟨depositᵢ.contribution⟩ ) == contract.price
-check Deposit(⟨depositᵢ⟩)
+Check Sum ⟨depositᵢ.contribution⟩ == contract.price
+Check Deposit(⟨depositᵢ⟩)
msg = Gen-Msg(MERCHANT_PAYMENT_OK, h_contract)
sig = EdDSA-Sign(merchant.priv, msg)
]]></artwork>
@@ -616,7 +650,7 @@ sig = EdDSA-Sign(merchant.priv, msg)
(W3) payment verification (wallet)
msg = Gen-Msg(MERCHANT_PAYMENT_OK, h_contract)
-check EdDSA-Verify(merchant.pub, msg, sig)
+Check EdDSA-Verify(merchant.pub, msg, sig)
]]></artwork>
</section>
<section anchor="deposit">
@@ -625,10 +659,10 @@ check EdDSA-Verify(merchant.pub, msg, sig)
<t>Deposit could also be used directly by a wallet with its own payto and a minimal contract.</t>
<artwork><![CDATA[
merchant exchange
-knows exchange.pub knows exchange.priv
-knows merchant.priv knows ⟨denomᵢ⟩
-knows payto, wire_salt |
-knows contract, ⟨depositᵢ⟩ |
+Knows exchange.pub Knows exchange.priv
+Knows merchant.priv Knows ⟨denomᵢ⟩
+Knows payto, wire_salt |
+Knows contract, ⟨depositᵢ⟩ |
| |
+--------------------------+ |
| (M1) deposit preparation | |
@@ -665,8 +699,8 @@ sig = EdDSA-Sign(merchant.priv, msg)
h_wire = HKDF(info.wire.wire_salt, info.wire.payto, "merchant-wire-signature", 64)
for i in 0..n:
coinᵢ = depositᵢ.coin
- denomᵢ = Denom-Lookup(coinᵢ.h_denom)
- check denomᵢ known and not deposit-expired // todo: check could be included in Denom-Lookup
+ denomᵢ = Lookup by coinᵢ.h_denom
+ Check denomᵢ known and not deposit-expired // todo: check could be included in Denom-Lookup
totalᵢ = depositᵢ.contribution + denomᵢ.fee_deposit
msgᵢ = Gen-Msg(WALLET_COIN_DEPOSIT,
( h_contract | uint256(0x0)
@@ -674,18 +708,17 @@ for i in 0..n:
| info.time.timestamp | info.time.refund_deadline
| totalᵢ
| denomᵢ.fee_deposit | merchant.pub | uint512(0x0) ))
- check EdDSA-Verify(coinᵢ.pub, msgᵢ, depositᵢ.sig)
- check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
- check coinᵢ.value >= totalᵢ
- persist coinᵢ.value -= totalᵢ
-persist deposit-record
+ Check EdDSA-Verify(coinᵢ.pub, msgᵢ, depositᵢ.sig)
+ Check RSA-FDH-Verify(SHA-512(coinᵢ.pub), coinᵢ.sig, denomᵢ.pub)
+ Check-Subtract(coinᵢ.value, total)
+Persist deposit-record
schedule bank transfer to payto
timestamp = now()
msg = Gen-Msg(EXCHANGE_CONFIRM_DEPOSIT,
( h_contract | h_wire | uint512(0x0)
| timestamp | info.time.wire_deadline
| info.time.refund_deadline
- | sum( ⟨depositᵢ.contribution⟩ )
+ | Sum ⟨depositᵢ.contribution⟩
| SHA-512( ⟨depositᵢ.sig⟩ ) | merchant.pub ))
sig = EdDSA-Sign(exchange.priv, msg)
]]></artwork>
@@ -697,18 +730,19 @@ msg = Gen-Msg(EXCHANGE_CONFIRM_DEPOSIT,
( h_contract | h_wire | uint512(0x0)
| timestamp | contract.wire_deadline
| contract.refund_deadline
- | sum( ⟨depositᵢ.contribution⟩ )
+ | Sum ⟨depositᵢ.contribution⟩
| SHA-512( ⟨depositᵢ.sig⟩ ) | merchant.pub ))
-check EdDSA-Verify(exchange.pub, msg, sig)
+Check EdDSA-Verify(exchange.pub, msg, sig)
]]></artwork>
</section>
<section anchor="refresh">
<name>Refresh</name>
<t>// todo: add introductory text</t>
+ <t>// todo: factor out Derive (from shared secret onwards)</t>
<artwork><![CDATA[
wallet exchange
-knows ⟨denomᵢ⟩ knows ⟨denomᵢ.priv⟩
-knows coin |
+Knows ⟨denomᵢ⟩ Knows ⟨denomᵢ.priv⟩
+Knows coin |
| |
+-------------------+ |
| (W1) coin melting | |
@@ -759,52 +793,52 @@ for k in 0..κ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
for i in 0..n:
- h_denomᵢ = SHA-512(uint32(0) | uint32(0x1) | denomᵢ.pub)
+ h_denomᵢ = Hash-Denom(denomᵢ)
planchets = (⟨h_denomᵢ⟩, ⟨planchetₖᵢ⟩, ⟨transferₖᵢ.pub⟩))
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
sig = EdDSA-Sign(coin.priv, msg)
-persist (coin.denom.pub, ...) // todo: double-check
+Persist (coin.denom.pub, ...) // todo: double-check
]]></artwork>
<artwork><![CDATA[
(E1) gamma selection and coin signing (exchange)
-denom = Denom-Lookup(coin.h_denom)
-check denom known and not refresh-expired
-check RSA-FDH-Verify(SHA-512(coin.pub), coin.sig, denom.pub)
-check coin.pub known and dirty
+denom = Lookup by coin.h_denom
+Check denom known and not refresh-expired
+Check RSA-FDH-Verify(SHA-512(coin.pub), coin.sig, denom.pub)
+Check coin.pub known and dirty
(⟨h_denomᵢ⟩, ⟨planchetₖᵢ⟩, ⟨transferₖᵢ.pub⟩)) = planchets
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
- check denomᵢ known and not withdraw-expired
-value' = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
-check value' == value
-check coin.value >= value
-persist coin.value -= value
+ denomᵢ = Lookup by h_denomᵢ
+ Check denomᵢ known and not withdraw-expired
+value' = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
+Check value' == value
+Check-Subtract(coin.value, value)
for k in 0..κ:
for i in 0..n:
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
-check EdDSA-Verify(coin.pub, msg, sig)
-(ɣ, _, _, done, _) = lookup refresh-record(commitment)
-if refresh-record not found:
+Check EdDSA-Verify(coin.pub, msg, sig)
+refresh_record = Lookup by commitment
+(ɣ, _, _, done, _) = refresh_record
+if refresh_record not found:
ɣ = 0..κ at random
for i in 0..n:
blind_sigᵢ = RSA-FDH-Sign(planchetᵧᵢ, denomᵧᵢ.priv)
link_info = (refresh_seed, ⟨transferₖᵢ.pub⟩, ⟨h_denomᵢ⟩, coin_sig)
- persist refresh-record = (commitment, ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, false, link_info)
+ Persist refresh_record = (commitment, ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, false, link_info)
msg = Gen-Msg(EXCHANGE_CONFIRM_MELT,
( commitment | uint32(ɣ) ))
sig = EdDSA-Sign(exchange.priv, msg)
@@ -812,19 +846,20 @@ sig = EdDSA-Sign(exchange.priv, msg)
<artwork><![CDATA[
(W2) secret revelation (wallet)
-check exchange.pub known
+Check exchange.pub known
msg = Gen-Msg(EXCHANGE_CONFIRM_MELT,
( commitment | ɣ ))
-check EdDSA-Verify(exchange.pub, msg, sig)
-persist refresh-challenge // what exactly?
+Check EdDSA-Verify(exchange.pub, msg, sig)
+Persist refresh-challenge // what exactly?
for k in 0..κ and k != ɣ:
revealed_seedₖ = batch_seedₖ
]]></artwork>
<artwork><![CDATA[
(E2) commitment validation (exchange)
-(ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, done, _) = lookup refresh-record(commitment)
-check not done // todo: sure?
+refresh_record = Lookup by commitment
+(ɣ, ⟨blind_sigᵢ⟩, h_planchetsᵧ, done, _) = refresh_record
+Check not done // todo: sure?
for k in 0..κ and k != ɣ:
⟨transferₖᵢ.priv⟩ = HKDF("refresh-transfer-private-keys", batch_seedₖ, "", n*32)
for i in 0..n:
@@ -835,29 +870,29 @@ for k in 0..κ and k != ɣ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment' = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
-check commitment == commitment'
-persist refresh-record = (_, _, _, true, _)
+Check commitment == commitment'
+Persist refresh_record = (_, _, _, true, _)
]]></artwork>
<artwork><![CDATA[
(W3) coin unblinding (wallet)
for i in 0..n:
coinᵧᵢ.sig = RSA-FDH-Unblind(blind_sigᵧᵢ, blind_secretᵧᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
coinᵧᵢ.h_denom = h_denomᵢ
- persist ⟨coinᵧᵢ⟩
+ Persist ⟨coinᵧᵢ⟩
]]></artwork>
<section anchor="link">
<name>Link</name>
<t>// todo: add introductory text</t>
<artwork><![CDATA[
wallet exchange
-knows coin knows refresh-record for coin
+Knows coin Knows refresh_record for coin
| |
+----------------------+ |
| (W1) history request | |
@@ -887,7 +922,8 @@ sig = EdDSA-Sign(coin.priv, msg)
<artwork><![CDATA[
(E1) refresh secret lookup (exchange)
-(ɣ, ⟨blind_sigᵢ⟩, _, done, link_info) = lookup refresh-record(coin.pub)
+refresh_record = Lookup by coin.pub
+(ɣ, ⟨blind_sigᵢ⟩, _, done, link_info) = refresh_record
if done:
melt_info = (ɣ, link_info, ⟨blind_sigᵢ⟩)
else:
@@ -900,7 +936,7 @@ else:
(refresh_seed, ⟨transferₖᵢ.pub⟩, ⟨h_denomᵢ⟩, coin_sig) = link_info
for i in 0..n:
- denomᵢ = Denom-Lookup(h_denomᵢ)
+ denomᵢ = Lookup by h_denomᵢ
for k in 0..κ:
for i in 0..n:
sharedₖᵢ = ECDH-EdDSA(coin.priv, transferₖᵢ.pub)
@@ -909,22 +945,22 @@ for k in 0..κ:
coinₖᵢ.priv = HKDF("coin", planchet_seedₖᵢ, "", 32)
coinₖᵢ.pub = EdDSA-GetPub(coinₖᵢ.priv)
planchetₖᵢ = RSA-FDH-Blind(SHA-512(coinₖᵢ.pub), blind_secretₖᵢ, denomᵢ.pub)
- h_planchetₖᵢ = SHA-512( SHA-512( denomᵢ.pub ) | uint32(0x1) | planchetₖᵢ )
+ h_planchetₖᵢ = Hash-Planchet(planchetₖᵢ, denomᵢ)
h_planchetsₖ = SHA-512( ⟨h_planchetₖᵢ⟩ )
-value = coin.denom.fee_refresh + sum( ⟨denomᵢ.value⟩ ) + sum( ⟨denomᵢ.fee_withdraw⟩ )
+value = coin.denom.fee_refresh + Sum ⟨denomᵢ.value⟩ + Sum ⟨denomᵢ.fee_withdraw⟩
commitment = SHA-512( refresh_seed | uint256(0x0) | coin.pub | value
| SHA-512( ⟨h_planchetsₖ⟩ ) )
msg = Gen-Msg(WALLET_COIN_MELT,
( commitment | coin.h_denom | uint256(0x0)
| value | denom.fee_refresh ))
-check EdDSA-Verify(coin.pub, msg, sig)
+Check EdDSA-Verify(coin.pub, msg, sig)
if ⟨blind_sigᵢ⟩ returned:
for i in 0..n:
coinᵧᵢ.sig = RSA-FDH-Unblind(blind_sigᵧᵢ, blind_secretᵧᵢ, denomᵢ.pub)
- check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
+ Check RSA-FDH-Verify(SHA-512(coinᵧᵢ.pub), coinᵧᵢ.sig, denomᵢ.pub)
coinᵧᵢ.h_denom = h_denomᵢ
- persist ⟨coinᵧᵢ⟩
+ Persist ⟨coinᵧᵢ⟩
]]></artwork>
</section>
</section>
@@ -1032,7 +1068,7 @@ if ⟨blind_sigᵢ⟩ returned:
<refcontent>National Institute of Standards and Technology (U.S.)</refcontent>
</reference>
</references>
- <?line 1061?>
+ <?line 1079?>
<section anchor="change-log">
<name>Change log</name>
@@ -1045,190 +1081,199 @@ Education and Research (BMBF) within the project Concrete Contracts.</t>
</section>
</back>
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